“平面”重言式难以分辨

Proceedings 2001 IEEE International Conference on Cluster Computing Pub Date : 2001-10-14 DOI:10.1109/SFCS.2001.959896

Stefan S. Dantchev, Søren Riis

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引用次数: 26

摘要

在矩形网格图的基础上，我们证明了一些重言式的分辨率证明的指数下界。更具体地说，我们展示了一个2/sup /spl Omega/(n)/下界，适用于在2n/spl次/2n棋盘上残废棋盘问题的任何分辨率证明，以及基于n/spl次/n矩形网格图的tseittin重言式(G. tseittin, 1968)。前一个结果回答了J. McCarthy(1964) 35年前的猜想。

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"Planar" tautologies hard for resolution

We prove exponential lower bounds on the resolution proofs of some tautologies, based on rectangular grid graphs. More specifically, we show a 2/sup /spl Omega/(n)/ lower bound for any resolution proof of the mutilated chessboard problem on a 2n/spl times/2n chessboard as well as for the Tseitin tautology (G. Tseitin, 1968) based on the n/spl times/n rectangular grid graph. The former result answers a 35 year old conjecture by J. McCarthy (1964).

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Proceedings 2001 IEEE International Conference on Cluster Computing

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